Object texture not showing up when selecting "texture" viewport shading
Found the answer:

When using Blender Render, you only need to UV unwrap an object and add a picture to make it show up in texture viewport. 
  When using Cycles, you need to do as in BR and then add a material, go to node editor and add an image texture. Select the picture you UV unwrapped the object to, and without connecting the node anywhere, the texture shows up in viewport texture mode.